Singularities in cosmological loop correlators. Part II. Non local interactions and flat space limits

Abstract

Non-local interactions naturally arise in the ADM formalism after solving the constraint equations and substituting their solutions back into the action. However, the effects of these non-local operators on loop corrections to cosmological correlators remain largely unexplored. Extending the analysis of [1], in this work we compute the 1-loop bispectrum during slow-roll inflation, including the inverse-Laplacian operators present at cubic and quartic order in the ADM action (in the spatially flat gauge). These non-local vertices introduce non-trivial angular dependencies that significantly complicate the evaluation of loop integrals. We find that the diagrammatic rules of [1] for identifying poles and branch cuts in correlators without explicit integration remain valid even in the presence of such non-local interactions. Finally, we derive the flat-space limit of the 1-loop inflationary correlator and verify it with explicit examples, thereby establishing a direct correspondence between its leading total-energy singularities (ωT → 0) and the flat-space scattering amplitude.